Answer:
[tex]\sf 2x - 3 = -5x^2[/tex]
move terms to one side:
[tex]\sf 2x - 3 = -5x^2=0[/tex]
Split second term in 2x-3+5x^2 into two terms:
[tex]\sf 5x^2+5x-3x-3=0[/tex]
factor out common terms in first terms, then last terms
[tex]\sf 5x(x+1)-3(x+1)=0[/tex]
Factor out common term: x+1
[tex](x+1)(5x-3)=0[/tex]
solve for x
[tex]\sf x+1=0[/tex]
- [tex]\boxed{\sf x=-1}[/tex]
[tex]\sf 5x-3=0[/tex]
- [tex]\sf 5x-3+3=0+3[/tex]
- [tex]\sf \cfrac{5x}{5}=\cfrac{3}{5}[/tex]
- [tex]\boxed{\sf x=\frac{3}{5}}[/tex]
[tex]\boxed{\sf Answer: x=-1,\:x=\frac{3}{5}}[/tex]
